International Electronic Journal of Mathematics Education

Influence of Domain-General Abilities and Prior Division Competence on Fifth-Graders’ Fraction Understanding
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Stelzer F, Andrés ML, Canet-Juric L, Urquijo S, Richards MM. Influence of Domain-General Abilities and Prior Division Competence on Fifth-Graders’ Fraction Understanding. Int Elect J Math Ed. 2019;14(3), 489-500. https://doi.org/10.29333/iejme/5751
APA 6th edition
In-text citation: (Stelzer et al., 2019)
Reference: Stelzer, F., Andrés, M. L., Canet-Juric, L., Urquijo, S., & Richards, M. M. (2019). Influence of Domain-General Abilities and Prior Division Competence on Fifth-Graders’ Fraction Understanding. International Electronic Journal of Mathematics Education, 14(3), 489-500. https://doi.org/10.29333/iejme/5751
Chicago
In-text citation: (Stelzer et al., 2019)
Reference: Stelzer, Florencia, María Laura Andrés, Lorena Canet-Juric, Sebastián Urquijo, and María Marta Richards. "Influence of Domain-General Abilities and Prior Division Competence on Fifth-Graders’ Fraction Understanding". International Electronic Journal of Mathematics Education 2019 14 no. 3 (2019): 489-500. https://doi.org/10.29333/iejme/5751
Harvard
In-text citation: (Stelzer et al., 2019)
Reference: Stelzer, F., Andrés, M. L., Canet-Juric, L., Urquijo, S., and Richards, M. M. (2019). Influence of Domain-General Abilities and Prior Division Competence on Fifth-Graders’ Fraction Understanding. International Electronic Journal of Mathematics Education, 14(3), pp. 489-500. https://doi.org/10.29333/iejme/5751
MLA
In-text citation: (Stelzer et al., 2019)
Reference: Stelzer, Florencia et al. "Influence of Domain-General Abilities and Prior Division Competence on Fifth-Graders’ Fraction Understanding". International Electronic Journal of Mathematics Education, vol. 14, no. 3, 2019, pp. 489-500. https://doi.org/10.29333/iejme/5751
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Stelzer F, Andrés ML, Canet-Juric L, Urquijo S, Richards MM. Influence of Domain-General Abilities and Prior Division Competence on Fifth-Graders’ Fraction Understanding. Int Elect J Math Ed. 2019;14(3):489-500. https://doi.org/10.29333/iejme/5751

Abstract

The present study analyzed the relationship between domain-general abilities and fraction knowledge in fifth grade, and investigated the mediating role of division competence in that relationship. Children (n = 175) were assessed in fourth grade on domain-general abilities (selective attention, working memory, fluid intelligence) and on division competence; and in fifth grade on fraction conceptual knowledge. Mediation analyses revealed that domain general abilities were direct predictors of fraction concepts, and division competence mediates the 32% of the effect of working memory and the 17% of the effect of intelligence on fraction knowledge. These findings support the assumptions of those theoretical models of numerical cognition that proposed a central role of general cognitive abilities for mathematics learning and indicate that there are distinct pathways from general cognitive abilities to fraction conceptual knowledge.

References

  • Baddeley, A. D., & Hitch, G.J. (1974). Working memory. In G.A. Bower (Ed.), The Psychology of Learning and Motivation: Advances in Research and Theory (pp. 47–89). New York: Academic.
  • Baddeley, A. (2012). Working Memory: Theories, Models, and Controversies. Annual Review of Psychology, 63, 1-29. https://doi.org/10.1146/annurev-psych-120710-100422
  • Bailey, D. H., Siegler, R. S., & Geary, D. C. (2014). Early predictors of middle school fraction knowledge. Developmental Science, 17(5), 775-785. https://doi.org/10.1111/desc.12155
  • Baron, R. M., & Kenny, D. A. (1986). The mediator–moderator distinction in social psychology: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173–1182.
  • Booth, J. L., & Newton, K. J. (2012). Fractions: Could they really be the gatekeeper’s doorman?. Contemporary Educational Psychology, 37(4), 247–253. https://doi.org/10.1016/j.cedpsych.2012.07.001
  • Booth, J. L., Newton, K. J., & Twiss-Garrity, L. K. (2014). The impact of fraction magnitude knowledge on algebra performance and learning. Journal of Experimental Child Psychology, 118, 110–118. https://doi.org/10.1016/j.jecp.2013.09.001
  • Brown, B. W. (1991). How gender and socioeconomic status affect reading and mathematics achievement. Economics of Education Review, 10(4), 343-357.
  • Canet Juric, L., Introzzi, I., & Burin, D. (2015). Desarrollo de la Capacidad de Memoria de Trabajo Efectos de Interferencia Inter e Intra Dominio en Niños de Edad Escolar. Revista Argentina de Ciencias del Comportamiento, 7(1), 26–37.
  • Carpenter, T., Corbitt, M., Kepner, H., Lindquist, M., & Reys, R. (1980). Results of the second NAEP mathematics assessment: Secondary school. Mathematics Teacher, 73, 329-338.
  • Cattell, R. B. (1971). Abilities: their structure, growth, and action. Boston: Houghton.
  • Cayssials, A. (1993). Test de Matrices Progresivas. Manual adaptación Argentina. Buenos Aires: Paidós.
  • Chan, W.-H., Leu, Y.-C., & Chen, C.-M. (2007). Exploring group-wise conceptual deficiencies of fractions for fifth and sixth graders in Taiwan. Journal of Experimental Education, 76, 26–57. https://doi.org/10.3200/JEXE.76.1.26-58
  • Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64 (3), 293-316. https://doi.org/10.1007/s10649-006-9036-2
  • DeWolf, M., Bassok, M., & Holyoak, K. J. (2015). From rational numbers to algebra: Separable contributions of decimal magnitude and relational understanding of fractions. Journal of Experimental Child Psychology, 13, 72-84. https://doi.org/10.1016/j.jecp.2015.01.013
  • DeWolf, M., Bassok, M., & Holyoak, K. J. (2016). A set for relational reasoning: Facilitation of algebraic modeling by a fraction task. Journal of Experimental Child Psychology, 152, 351–366. https://doi.org/10.1016/j.jecp.2016.06.016
  • Diamond, A. (2013). Executive functions. Annual Review of Psychology, 64, 135-168. https://doi.org/10.1146/annurev-psych-113011-143750
  • Dirección General de Cultura y Educación (2018). Diseño curricular para la educación primaria: primer ciclo y segundo ciclo (1a ed). La Plata: Dirección General de Cultura y Educación de la Provincia de Buenos Aires. [General Management of Culture and Education (2018). Curricular design for primary education: first cycle and second cycle (1st ed). La Plata: General Management of Culture and Education of Buenos Aires Province.] Retrieved from http://servicios.abc.gov.ar/lainstitucion/organismos/consejogeneral/disenioscurriculares/primaria/2018/dis-curricular-PBA-completo.pdf
  • Engle, R. W. (2002). Working memory capacity as executive attention. Current Directions in Psychological Science, 11, 19–23. https://doi.org/10.1111/1467-8721.00160
  • Engle, R. W., & Kane, M. J. (2004). Executive attention, working memory capacity, and a two-factor theory of cognitive control. In B. Ross (Ed.), The psychology of learning and motivation (pp. 145–199). New York, NY: Academic Press.
  • Flotts, M. P., Manzi, J., Jiménez, D., Abarzúa, A., Cayuman, C., & García, M. J. (2016). Informe de resultados TERCE. Retrieved from http://unesdoc.unesco.org/images/0024/002435/243532S.pdf
  • Fuchs, M. W., Hornburg, C. B., & McNeil, N. M. (2016). Specific early number skills mediate the association between executive functioning skills and mathematics achievement. Developmental Psychology, 52(8), 1217-1235. https://doi.org/10.1037/dev0000145
  • Gabriel, F. C., Coché, F., Szucs, D., Carette, V., Rey, B., & Content, A. (2013). A componential view of children’s difficulties in learning fractions. Frontiers in Psychology, 4, 715. https://doi.org/10.3389/fpsyg.2013.00715
  • Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4–15. https://doi.org/10.1177/00222194040370010201
  • Geary, D. C. (2006). Development of mathematical understanding. In D. Kuhl, R. S. Siegler (Vol. Eds.), Cognition, perception, and language. W. Damon (Gen Ed.), Handbook of child psychology (6th ed., pp. 777–810). New York: John Wiley & Sons. https://doi.org/10.1002/9780470147658.chpsy0218
  • Geary, D. C., Boykin, A. W., Embretson, S., Reyna, V., Siegler, R., Berch, D. B., & Graban, J. (2008). Report of the task group on learning processes. National mathematics advisory panel, reports of the task groups and subcommittees, 4-1. Retrieved from https://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf
  • Geary, D., Nicholas, A., Li, Y., & Sun, J. (2017). Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement: An Eight-Year Longitudinal Study. Journal of Educational Psychology, 109(5), 680–693. https://doi.org/10.1037/edu0000159
  • Hansen, N., Jordan, N. C., Fernandez, E., Siegler, R. S., Fuchs, L., Gersten, R., & Micklos, D. (2015). General and math-specific predictors of sixth-graders’ knowledge of fractions. Cognitive Development, 35, 34-49. https://doi.org/10.1016/j.cogdev.2015.02.001
  • Hasher, L., Lustig, C., & Zacks, R. T. (2007). Inhibitory mechanisms and the control of attention. In A. Conway, C. Jarrold, M. Kane, A. Miyake, A., & J. Towse (Eds.), Variation in working memory (pp. 227-249). New York: Oxford University Press.
  • Hecht, S. A., & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology, 102(4), 843–59. https://doi.org/10.1037/a0019824
  • Hollingshead, A. B. (2011). Four Factor Index of Social Status. Yale Journal of Sociology, 8, 21–52.
  • Introzzi, I., & Canet Juric, L. (2013).Tareas de Autorregulación Cognitiva. En Introzzi, I., Canet Juric, L., Comesaña, A., Andres, M. L. & Richards, M. (2013). Evaluación de la Autorregulación cognitiva y emocional. Presentación de un Programa. Revista Argentina de Ciencias del Comportamiento (suplemento), 1-11.
  • Jordan, N., Hansen, N., Fuchs, L., Siegler, R., Gersten, R., & Micklos, D. (2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116(1), 45–58. https://doi.org/10.1016/j.jecp.2013.02.001
  • Kane, M. J., & Gray, J. R. (2005). Fluid intelligence. In N. J. Salkind (Ed.), Encyclopedia of Human Development (pp. 528−529). California: Sage Publications.
  • Kieren, T. E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. Lesh (Ed.), Number and Measurement: Papers from a Research Workshop ERIC/SMEAC (pp. 101–144). Columbus: OH.
  • LeFevre, J. A., Berrigan, L., Vendetti, C., Kamawar, D., Bisanz, J., Skwarchuk, S. L., & Smith-Chant, B. L. (2013). The role of executive attention in the acquisition of mathematical skills for children in Grades 2 through 4. Journal of Experimental Child Psychology, 114(2), 243-261. https://doi.org/10.1016/j.jecp.2012.10.005
  • LeFevre, J. A., Fast, L., Skwarchuk, S. L., Smith‐Chant, B. L., Bisanz, J., Kamawar, D., & Penner‐Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child Development, 81(6), 1753-1767. https://doi.org/10.1111/j.1467-8624.2010.01508.x
  • Locuniak, M. N., & Jordan, N. C. (2008). Using kindergarten number sense to predict calculation fluency in second grade. Journal of Learning Disabilities, 41, 451–459. https://doi.org/10.1177/0022219408321126
  • McGrew, K. S. (2009). CHC theory and the human cognitive abilities project: Standing on the shoulders of the giants of psychometric intelligence research. Intelligence, 37(490), 1−10. https://doi.org/10.1016/j.intell.2008.08.004
  • McGrew, K. S., & Evans, J. J. (2004). Internal and external factorial extensions to the Cattell–Horn–Carroll (CHC) theory of cognitive abilities: A review of factor analytic research since Carroll’s Seminal 1993 Treatises. St. Cloud, MN: Institute for Applied Psychometrics.
  • Ministerio de Educación (2011). Núcleos de Aprendizajes Prioritarios Segundo Ciclo EGB / Nivel Primario. Retrieved from http://www.me.gov.ar/curriform/publica/nap/nap_egb2.pdf
  • Miyake, A., & Shah, P. (1999). Toward unified theories of working memory: Emerging general consensus, unresolved theoretical issues and future directions. In Miyake, A. & Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp.442-481). Cambridge: Cambridge University Press.
  • Namkung, J. M., & Fuchs, L. S. (2015). Cognitive predictors of calculations and number line estimation with whole numbers and fractions among at-risk students. Journal of Educational Psychology, 108(2), 214-228. https://doi.org/10.1037/edu0000055
  • Pascual, L., Galperín, C. Z., & Bornstein, M. H. (1993). La medición del nivel socioeconómico y la psicología evolutiva: El caso Argentino. Revista Interamericana de Psicologia/Interamerican Journal of Psychology, 27, 59–74.
  • Peng, P., Namkung, J., Barnes, M., & Sun, C. (2016). A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics. Journal of Educational Psychology, 108(4), 455. https://doi.org/10.1037/edu0000079
  • Raven, J. C. (1989). Test de Matrices Progresivas para la medida de la capacidad intelectual, de sujetos de 4 a 11 años. Buenos Aires: Paidós. [Raven Progessive Matrices test for IQ assessment in 4 to 11 years old subjets]
  • Resnick, I., Jordan, N. C., Hansen, N., Rajan, V., Rodrigues, J., Siegler, R. S., & Fuchs, L. S. (2016). Developmental growth trajectories in understanding of fraction magnitude from fourth through sixth grade. Developmental Psychology, 52(5), 746. https://doi.org/0.1037/dev0000102
  • Richards, M., Introzzi, I., Zamora, E., & Vernucci, S. (2017). Analysis of Internal and External Validity Criteria for a Computerized Visual Search Task. A pilot study. Applied Neuropsychology: Child, 110-119. https://doi.org/10.1080/21622965.2015.1083433
  • Richards, M. M., Vernucci, S., Zamora, E., Canet Juric, L., Introzzi, I., & Guardia, J. (2017). Contribuciones empíricas para la validez de grupos contrastados de la Batería de Tareas de Autorregulación Cognitiva (TAC). Interdisciplinaria, 34(1), 173-192.
  • Sautú, R. (1989). Teoría y técnica en la medición del status ocupacional: Escalas objetivas de Prestigio (Documento de Trabajo). Buenos Aires, Argentina: UBA Instituto de Ciencias Sociales.
  • Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., et al. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23, 691–697. https://doi.org/10.1177/0956797612440101
  • Siegler, R. S., & Lortie-Forgues, H. (2017). Hard lessons: Why rational number arithmetic is so difficult for so many people. Current Directions in Psychological Science, 26(4), 346-351. https://doi.org/10.1177/0963721417700129
  • Siegler, R. S., & Pyke, A. A. (2013). Developmental and individual differences in understanding of fractions. Developmental Psychology, 94(10), 1994–2004. https://doi.org/10.1037/a0031200
  • Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62, 273–296. https://doi.org/10.1016/j.cogpsych.2011.03.001
  • Sowinski, C., LeFevre, J.A., Skwarchuk, S. L., Kamawar, D., Bisanz, J., & Smith-Chant, B. (2015). Refining the quantitative pathway of the Pathways to Mathematics model. Journal of Experimental Child Psychology, 131, 73–93. https://doi.org/10.1016/j.jecp.2014.11.004
  • Stelzer, F., Introzzi, I., Andres, M. L., Richard’s, M., & Urquijo (2018). Factores cognitivos relacionados con la capacidad de cálculo de división en estudiantes de 4º año [Cognitive factors related to division ability in fourth grade students]. Actualidades investigativas en educación, 18(1), 1–26.
  • Thurstone, L. L., & Yela, M. (2012). CARAS-R. Test de percepción de diferencias-Revisado. Buenos Aires: TEA Ediciones.
  • Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2014). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, https://doi.org/10.1016/j.learninstruc.2014.03.002
  • van der Ven, S.H. G., van der Maas, H. L.J., Straatemeier , M., & Jansen, B. R. J. (2013). Visuospatial working memory and mathematical ability at different ages throughout primary school. Learning and Individual Differences, 27, 182–192. https://doi.org/10.1016/j.lindif.2013.09.003
  • Vukovic, R. K., Fuchs, L. S., Geary, D. C., Jordan, N. C., Gersten, R., & Siegler, R. S. (2014). Sources of individual differences in children’s understanding of fractions. Child Development, 85(4), 1461-1476. https://doi.org/10.1111/cdev.12218
  • Ye, A., Resnick, I., Hansen, N., Rodrigues, J., Rinne, L., & Jordan, N. C. (2016). Pathways to fraction learning: Numerical abilities mediate the relation between early cognitive competencies and later fraction knowledge. Journal of Experimental Child Psychology, 152, 242-263. https://doi.org/10.1016/j.jecp.2016.08.001

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